Many scientific and other applications depend on a set of data and their inter-relationship. The set of data is dependent normally on finite number of functions, which may or may not be inter dependent. Simplest way to understand the nature of an element in a set of data is to approach some of the statistical methods and find the relationships between them. The methods we consider are rank regression and use regression coefficients for a set of data to another set of data or find the ranks of each element of the set and understand the role of the particular element in the set. Studies are also available to Poison methods for models for probabilistic weighted retrieval methods (refer to Robertson, S. E., Walker. S., Some simple effective approximations to the 2 poison model for probabilistic weighted retrieval, in Proc. 17th Annual international ACM SIGIR Conference on Research and Development in Information Retrieval, Association for Computing Machinery, New York, 1994, pp 232-241.
Ranking is one of the most important applications in several areas of life. It is also considered through several angles such as complexity of calculation, relevance, precision and recall etc. There are very few methods established till now to understand the relevance of an element in its domain (please refer to Karen Sparck Jones, Information retrieval and artificial intelligence, Artificial Intelligence V 114 (1999), 257-281, Elsevier Publication).
A case study with Web page to a particular query was addressed by Karen Sparck Jones uses artificial methods for understanding of a web page in a finite set. Examples are given in the area of web pages since the web is considered as most dynamically growing environment and needs addressing from several directions. Calculation of relevance, quantifying the page properties such as term frequency, inverse document frequency are well related to a particular query or a key word to that page. The present study is aimed at finding the overall effect of a particular page in the set. Though the examples taken are from a sub set of WWW, this method can be applied to any function that is N-dimensional vector based and each axis of the quantity has specific physical meaning to it. Statistical methods fail in addressing these problems because of non-availability of quantitative relationship of a particular element to the group.